杨代数
在表示论中,杨代数(或杨子、Yangian)是一种无限维的霍普夫代数和量子群。这是以杨振宁命名的。俄罗斯物理学家弗拉基米尔·德林费尔德和路德维希·法捷耶夫首先研究了杨子。
定义
若a是半单李代数,Y(a)是无限维的霍普夫代数(跟泛包络代数有关系)。Y(a)是杨代数。
有些方程
若
若R-矩阵是 R(z)= I+ z-1 P
应用
阅读
- Chari, Vyjayanthi; Andrew Pressley. A Guide to Quantum Groups. Cambridge, U.K.: Cambridge University Press. 1994. ISBN 0-521-55884-0.
- Drinfeld, Vladimir Gershonovich. Алгебры Хопфа и квантовое уравнение Янга-Бакстера [Hopf algebras and the quantum Yang–Baxter equation]. Doklady Akademii Nauk SSSR. 1985, 283 (5): 1060–1064 (俄语).
- Drinfeld, V. G. A new realization of Yangians and of quantum affine algebras. Doklady Akademii Nauk SSSR. 1987, 296 (1): 13–17 (俄语). 翻译在 Soviet Mathematics - Doklady. 1988, 36 (2): 212–216. 缺少或
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为空 (帮助) - Drinfeld, V. G. Вырожденные аффинные алгебры Гекке и янгианы [Degenerate affine Hecke algebras and Yangians]. Funktsional'nyi Analiz I Ego Prilozheniya. 1986, 20 (1): 69–70. MR 0831053. Zbl 0599.20049 (俄语). 翻译在 Drinfeld, V. G. Degenerate affine hecke algebras and Yangians. Functional Analysis and Its Applications. 1986, 20 (1): 58–60. doi:10.1007/BF01077318.
- Molev, Alexander Ivanovich. Yangians and Classical Lie Algebras. Mathematical Surveys and Monographs. Providence, RI: American Mathematical Society. 2007. ISBN 978-0-8218-4374-1.
- Bernard, Denis. An Introduction to Yangian Symmetries. NATO ASI Series. 1993, 310 (5): 39–52. ISBN 978-1-4899-1518-4. arXiv:hep-th/9211133 . doi:10.1007/978-1-4899-1516-0_4.
- MacKay, Niall. Introduction to Yangian Symmetry in Integrable Field Theory. International Journal of Modern Physics A. 2005, 20 (30): 7189–7217. Bibcode:2005IJMPA..20.7189M. arXiv:hep-th/0409183 . doi:10.1142/s0217751x05022317.
- Drummond, James; Henn, Johannes; Plefka, Jan. Yangian Symmetry of Scattering Amplitudes in N = 4 super Yang-Mills Theory. Journal of High Energy Physics. 2009, 2009 (5): 046. Bibcode:2009JHEP...05..046D. arXiv:0902.2987 . doi:10.1088/1126-6708/2009/05/046.
参考文献
- ^ Beisert, N. (2007). The S-matrix of AdS/CFT and Yangian symmetry. arXiv preprint arXiv:0704.0400.
- ^ Spill, F. (2009). Weakly coupled N= 4 Super Yang-Mills and N= 6 Chern-Simons theories from u (2| 2) Yangian symmetry. Journal of High Energy Physics, 2009(03), 014, https://arxiv.org/abs/0810.3897 (页面存档备份,存于互联网档案馆)